UNCERTAINTY · Financial Decision Making under Multi-Dimentional Uncertainty

Financial Decision Making under Multi-Dimentional Uncertainty

During the recent decades it has become commonly agreeable that existing financial models cannot provide a complete explanation for many observable phenomena in the financial arena. One flaw of the existing models is that they do not capture the entire picture of uncertainty. Typically, asset pricing models focus on risk and assume away ambiguity----the uncertainty about probabilities. This research aims to generalize models of asset pricing to accommodate this additional tier of uncertainty, called ambiguity. It models financial decision-making in a more realistic manner by dropping the standard restrictive assumption that economic agents know the precise odds of possible events. The current research focuses on ambiguity and its implications for financial decision-making. It addresses a series of fundamental questions about the nature of ambiguity. For example: How is optimal-portfolio composition affected by ambiguity? Does ambiguity lead to greater savings compared to the standard risk? When do ambiguity and risk reinforce (counteract) each other? Can ambiguity be eliminated or reduced by diversification in a manner similar to idiosyncratic risk? Can ambiguity and risk be diversified away simultaneously? Is the entire, systematic and idiosyncratic, ambiguity priced, or only its systematic component? Can the two components be separated? These questions, however, suggest an even more fundamental question: How can the degree of ambiguity be measured? To the best of my knowledge, the current research is the first to address this question. It provides an applicable measure of ambiguity that can be used in empirical studies. This measure paves the way for addressing all other challenges that this research faces. The outcome of this research is five working papers that deal with different empirical and theoretical aspects of ambiguity in the context of financial decision making and asset pricing. Selected abstracts follow. A Theoretical Foundation of Ambiguity Measurement: Ordering alternatives by their degree of ambiguity is a crucial element in decision making processes in general and in asset pricing in particular. Thus far the literature has not provided an applicable measure of ambiguity allowing for such ordering. The current paper addresses this need by introducing a novel empirically applicable ambiguity measure derived from a new model of decision making under ambiguity in which probabilities of events are themselves random. In this model a complete distinction is attained between preferences and beliefs and between risk and ambiguity that enables the degree of ambiguity to be measured. A merit of the model is that ambiguous probabilities can be incorporated into asset prices and an ambiguity premium can be measured empirically. Capital Asset Pricing under Ambiguity: This paper generalizes the standard mean–variance paradigm to a mean–variance–ambiguity paradigm by relaxing the assumption that probabilities are known and instead assuming that probabilities are themselves random. It extends the CAPM from risk to uncertainty by incorporating ambiguity. This model makes the distinction between systematic ambiguity and idiosyncratic ambiguity and proves that the ambiguity premium is proportional to systematic ambiguity. It introduces a new measure of uncertainty that combines risk and ambiguity. Use of this model can be extended to other applications including portfolio selection and performance measurement. Does Ambiguity Diversification Pay?: With a focus on risk, classical portfolio theory assumes that probabilities of future outcomes are known. In reality, however, there is ambiguity in these probabilities. This paper studies the nature of the relationship between risk and ambiguity and proves that in most cases ambiguity cannot be diversified without increasing risk. This insight implies that holding a fully diversified portfolio is not necessarily optimal. It challenges the conventional wisdom which asserts that investors should hold such a portfolio. Pricing Systematic Ambiguity in Capital Markets, co-authored with Menachem Brenner: Asset pricing models assume that probabilities of future outcomes are known. In reality, however, there is ambiguity with regard to these probabilities. Accounting for ambiguity in asset pricing theory results in a model with two systematic components, beta risk and beta ambiguity. The focus of this paper is to study the empirical implications of ambiguity for the cross section of equity returns. We find that systematic ambiguity is an important determinant of equity returns. We also find that the Fama-French factors contribute to the explanatory power of the two main drivers of returns; namely, systematic risk and systematic ambiguity. In addition to the five working papers described above, the outcome of this research project includes a few financial models. These (mainly theoretical) asset pricing models are in the process of being written as standalone manuscripts that can be sent for publication in academic journals. Brief descriptions follow. Option pricing: This model introduces ambiguity to the classical Black-Scholes option pricing model. It suggests that the price of an option is not only a function of the risk of its underlying asset, but also a function of the ambiguity of its underlying asset. Term structure of interest rate: This model contracts the pricing kernel for the case of uncertain (ambiguous) probabilities. Using this kernel, it extracts a stochastic discount factor under ambiguity and uses it to derive the term structure of interest rate in a general equilibrium model. Saving behavior: This model formulates the optimal portfolio selection and the optimal saving strategy under ambiguity. It accounts for the investor’s characteristics, including his preferences concerning risk and concerning ambiguity. Representative Agent under Ambiguity: This model aggregates the decision makers’ preferences concerning risk and ambiguity, as well as their beliefs, and identifies the preferences and the beliefs of the representative agent.

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